Boundary slopes of 2-bridge links determine the crossing number

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dc.creatorHoste, Jim E.
dc.creatorShanahan, Patrick D.
dc.date2006-03-09
dc.date.accessioned2026-07-07T07:06:41Z
dc.date.available2026-07-07T07:06:41Z
dc.descriptionA diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of the boundary of M. We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found by Hatcher and Thurston. Using this formula we show that the diameter of a 2-bridge link, that is, the difference between the smallest and largest finite slopes of diagonal surfaces, is equal to the crossing number.
dc.description16 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/0603206
dc.identifierhttp://arxiv.org/abs/math/0603206
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110115
dc.subjectGeometric Topology
dc.subjectCombinatorics
dc.subject57M25
dc.titleBoundary slopes of 2-bridge links determine the crossing number
dc.typetext

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